Computational Details:

As stated in the main text, density function theory using the generalized gradient approximation (GGA-PBE)is used for this study.An energy cutoff of 400 eV is used for the plane wave basis set. Graphene nanoribbons (GNRs) are represented as periodic systems with 4 C pairs in the lateral (repeated) direction (shown previously to be an efficient choice for Fe adsorption and defects on GNRs 1,2) and 5, 6, or 7 C pairs through the GNR width (n=5,6,7). A vacuum of greater than 15Å between periodic ribbons is maintained in all directions to limit self-interactions. Monkhorst-Pack k-point meshes of 9x1x1 were found to be sufficient to converge cells to less than 1 meV for the total system in agreement with similar cell sizes in previous studies1-3. This value is also the ionic convergence criteria used in all simulations. Defect sites are labeled according to their distance from the GNR edge (Figure 1of the main text for n=7). In these calculations, atoms are treated as spin polarized and edge C/N atoms and Fe atoms are initialized to have magnetic moments

Vacancy formation energy is calculated using a graphene C reference state as shown in Equation S1:

/ S1

In the case of an edge vacancy, the edge H is retained as shown in Figure 1aof the main text. In the case of pyridinic vacancies, a free N2 molecule in vacuum is used as the nitrogen reference state and defect formation energy is calculated using Equation S2:

/ S2

Formation energy for defects with Fe follow Equations S1 and S2 with the initial energy being that of the GNR+defect+Fe system energy and including the subtraction of the EFe,free reference state.

For Fe binding energy, a free Fe atom in vacuum is used as the Fe reference state leading to Equations S3 (no N) and S4 (with N):

/ S3
/ S4

Vacancy concentrations, cvac as a function of defect position, x, is given in Equation S4:

/ S4

This equation applies to pyridinic vacancies as well.

Concentration of Fe/vacancies,cvac-Fe , as a function of position is likewise proportional to the exponential of the defect formation energy. This is broken apart into a term associated with the formation of the vacancy and a term associated with the Fe binding energy. Thus, Equation S5 shows that the concentration of Fe/vacancy defects is proportional to the vacancy concentration and the exponential of the binding energy. This equation applies to Fe/pyridinic vacancies as well.

/ S5

Magnetic State Considerations:

In the case of Fe free defects, symmetry requires that only half of the GNR width be explored dictating ferromagnetic, FM, and anti-ferromagnetic, AFM, initial states for each symmetry inequivalent defect site on each GNR simulated. The presence of Fe breaks the magnetic symmetry (as Fe’s magnetic moment may couple to the nearest edge), necessitating exploration of the full width of sites in the case of AFM edge systems and two FM states, one where Fe and the edge states are aligned and one where the Fe and edge states are anti-aligned. Particular attention is paid to simulating the same relaxed structure in these different magnetic configurations states so as to avoid the meta-stable states that are prolific in these systems. Each relaxed structure was initialized with all symmetry inequivalent AFM/FM orderings and re-relaxed with the most stable structure at these different magnetic states to find the true ground state. Such a treatment was found to generate lower energy structures vs. relaxing initial defect structures with given initial magnetic orderings.

In agreement with previous studies4,5, it is found that the AFM ordering of edge states in the undefected GNRs yields the lowest energy. Also, as found previously6, the discrepancy in energies between the AFM and non-magnetic (and FM) states becomes larger as the GNR width is increased.

SI References:

1R. C. Longo, J. Carrete, J. Ferrer, and L. J. Gallego, Physical Review B 81 (11), 115418 (2010).

2R.C. Longo, J. Carrete, and L.J. Gallego, Journal of Chemical Physics 134 (2), 024704 (2011).

3R. C. Longo, J. Carrete, and L. J. Gallego, Physical Review B 83 (23), 235415 (2011).

4De-en Jiang, Bobby G. Sumpter, and Sheng Dai, The Journal of Chemical Physics 126 (13), 134701 (2007).

5Erjun Kan, Hongjun Xiang, Fang Wu, Changhoon Lee, Jinlong Yang, and Myung-Hwan Whangbo, Applied Physics Letters 96 (10), 102503 (2010).

6L. Pisani, J. A. Chan, B. Montanari, and N. M. Harrison, Physical Review B 75 (6), 064418 (2007).

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